One time only purchases

Does anyone know how we can set up an ecommerce system that can limit purchases to one per customer? We'd need to use PayPal. We are trying to sell tickets and limit the online purchases to one pair (two tickets) per customer.

Obviously we can limit the quantity, say in a drop down , to 2, but that would not stop people from repeating the process.

We'd be okay if they bought again using another name, but otherwise want to limit purchases to one time per customer.